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Mathematics
Problem
The answers are in Chapter 24. 3. Find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
if
4
sin
(
x
2
)
=
3
y
−
y
2
4 \sin \left(x^{2}\right)=3 y-y^{2}
4
sin
(
x
2
)
=
3
y
−
y
2
at
(
π
6
,
2
)
\left(\sqrt{\frac{\pi}{6}}, 2\right)
(
6
π
,
2
)
. (A)
−
4
π
6
-4 \sqrt{\frac{\pi}{6}}
−
4
6
π
(B)
4
π
6
\quad 4 \sqrt{\frac{\pi}{6}}
4
6
π
(C)
−
4
π
2
-4 \sqrt{\frac{\pi}{2}}
−
4
2
π
(D)
4
π
2
\quad 4 \sqrt{\frac{\pi}{2}}
4
2
π
(A)
−
4
π
6
-4 \sqrt{\frac{\pi}{6}}
−
4
6
π
(B)
4
π
6
\quad 4 \sqrt{\frac{\pi}{6}}
4
6
π
(C)
−
4
π
2
-4 \sqrt{\frac{\pi}{2}}
−
4
2
π
(D)
4
π
2
\quad 4 \sqrt{\frac{\pi}{2}}
4
2
π
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